# The Causal Uncertainty Principle: Manifold Tearing and the Topological Limits of Counterfactual Interventions

arXiv: https://arxiv.org/abs/2603.17385 · HTML: https://mlsanity.com/paper/2603.17385/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 19 references that are in the map.
- First posted on arXiv 18 Mar 2026.

## Builds on (most cited first, 7 of 7)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)

## Abstract (arXiv)

Judea Pearl's do-calculus provides a foundation for causal inference, but its translation to continuous generative models remains fraught with geometric challenges. We establish the fundamental limits of such interventions. We define the Counterfactual Event Horizon and prove the Manifold Tearing Theorem: deterministic flows inevitably develop finite-time singularities under extreme interventions. We establish the Causal Uncertainty Principle for the trade-off between intervention extremity and identity preservation. Finally, we introduce Geometry-Aware Causal Flow (GACF), a scalable algorithm that utilizes a topological radar to bypass manifold tearing, validated on high-dimensional scRNA-seq data.